Calculus Archive: Questions from April 21, 2023
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[11/2 ptos] Una partícula se desplaza a lo largo de una elipse dada por la ecuación \[ 4 x^{2}+9 y^{2}=36 \] cuando alcanza la coordenada \( (-2, b) \) con \( b>0 \), la abscisa aumenta con una rapi2 answers -
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1. Trace el punto de la coordenada polar y halle las coordenadas cartesianas de ese punto. \[ \left(-2,-\frac{5 \pi}{6}\right) \]2 answers -
\( \int \sin (7 x) d x \quad \int \csc ^{2}\left(\frac{x}{5}\right) d x \quad \int \frac{2}{x} d x \quad \int 15 \sec ^{2}(5 x) d x \)2 answers -
4. Determinar la ecuación de la línea tangente a \[ r=\operatorname{sen}(3 \theta) \text { en } \theta=\frac{\pi}{6} \] 5. Dibuje la curva y halle el área que encierra \[ r=2+\cos (2 \theta) \]2 answers -
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I. Evalủe el integral cambiando a coordenadas polares a) \( \int_{-1}^{1} \int_{0}^{\sqrt{1-x^{2}}} \cos \left(x^{2}+y^{2}\right) d y d x \) b) \( \int_{0}^{3} \int_{0}^{\sqrt{9-x^{2}}}\left(x^{2}+y2 answers -
\( \begin{array}{l}\text { Find } \int_{\text {ind }}(x+1)^{\frac{1}{4}} d x \\ \text { 2) } \int_{0}^{1} 7 x\left(\cos \left(x^{2}\right)\right) d x \\ \text { 3) } f(x) \text { if } f^{\prime}(x)=22 answers -
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Solo el inciso d) y e).
3) Evalúa las siguientes integrales de línea: a) \( \oint_{C} x^{2} y d x-y^{2} x d y \) donde \( \mathrm{C} \) es la circunferencia \( x^{2}+y^{2}=1 . \quad \) Respuesta \( -\pi / 2 \). b) \( \oint2 answers -
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Consider the function. \[ f(x, y, z)=x \sqrt{y+6 z} e^{z / x} \] Determine the domain of the function. \[ \begin{array}{l} \mathcal{D}=\{(x, y, z): x \neq 0, y \geq-6 z\} \\ \mathcal{D}=\{(x, y, z): x2 answers -
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